Constrained optimization of metabolic cost in human hopping

Constrained optimization of metabolic cost/distance travelled largely predicts the gait parameters selected by humans during walking and running. This study evaluates whether this is also the case for human hopping. Hop frequency (f), height (h) and metabolic energy expenditure were measured in partly constrained (f, h or hop speed, s ≡ fh, specified), fully constrained (both f and h specified) and unconstrained conditions (neither f nor h specified) for 4 min trials. Hop frequency and height were also measured in frequency-constrained (f specified), fully constrained (maximal height and f specified) and unconstrained conditions for 15 s trials. Metabolic cost surfaces were constructed from experimental data from the 4 min trials, and the least costly behaviour for each constraint was calculated. Subjects selected the same height-frequency pattern for all three partly constrained conditions because the metabolic cost/height surface for hopping was a slope with no observed minimum. The heights selected for the 15 s frequency-constrained trials were only slightly lower than maximal, the optimal behaviour predicted by constrained optimization of metabolic cost/height. This supports the hypothesis that constrained optimization of metabolic cost largely predicts movement selection during hopping. However, subjects often chose noticeably lower than optimal heights and higher than optimal frequencies during partly constrained and unconstrained conditions for the 4 min trials. It appears that they selected heights and frequencies that incurred a slightly greater metabolic cost/height in order to reduce metabolic cost/time to a level they could comfortably sustain for 4 min.